Electrooptic TIR light modulator image bar having electrode length for optimizing spatial frequency response

ABSTRACT

A technique for reducing interpixel crosstalk in an electrooptic total internal reflection light modulator image bar. A particular electrode length is selected to tailor a portion of the spatial frequency response of the image bar. The pixel size and quality resulting from a voltage difference between electrodes are determined primarily by the overall image bar spatial frequency response, and a set of preferred physical parameters can be determined by selecting parameter values to provide the desired spatial frequency response. It has been found that a desirable frequency response is one that approximates sin(πPf) for absolute values of f less than about 1/P, where f is the spatial frequency and P is the minimum pixel pitch. Further, it has been found that a particular electrode length provides the desired response for small absolute values of f. The particular electrode length is approximately E 1/2  P/γ where E is the ratio of the normal to tangential dielectric tensor components, P is the minimum pixel pitch, and γ is the grazing angle. The desired cutoff in the frequency response for absolute values of f above about 1/P can be achieved by selecting appropriate values for other physical parameters.

BACKGROUND OF THE INVENTION

The present invention relates generally to optical image bar printing,and more particularly to an electrode array configuration for an opticalimage bar.

As a matter of definition, an "optical image bar" comprises an array ofoptical pixel generators for converting a spatial pattern, which usuallyis represented by the information content of electrical input signals,into a corresponding optical intensity profile. Although there are avariety of applications for such devices and a number of differentfields, a significant portion of the effort and expense that have beendevoted to their development has been directed toward their applicationto electrophotographic printing.

One type of image bar is based on the use of electrooptic (EO) totalinternal reflection (TIR) spatial light modulators, as described in U.S.Pat. No. 4,396,252 to W. D. Turner, hereby incorporated by reference.The modulator comprises a set of laterally separated, individuallyaddressable electrodes, which are maintained closely adjacent areflective surface of an optically transparent EO element, such as alithium niobate crystal. In operation, substantially the full width ofthe EO element is illuminated by a transversely collimated light beam.This light beam is applied to the EO element at a near grazing angle ofincidence with respect to its reflective surface, and is brought to awedge-shaped focus on that surface so that it is totally internallyreflected therefrom.

Voltages representing a linear pixel pattern are applied to theindividually addressable electrodes, whereby localized fringe electricfields are coupled into the EO element. These fields produce localizedvariations in the refractive index of the EO element, so the wavefrontof the light beam is spatially phase modulated in accordance with thepixel pattern as it passes through the EO element. The process isrepeated for a sequence of pixel patterns, with the result that thewavefront of the light beam is spatially modulated as a function of timein accordance with successive ones of those patterns.

For image bar applications of such a modulator, schlieren optics areemployed to convert the phase modulated wavefront of the light beam intoa corresponding series of optical intensity profiles. If a printingfunction is being performed, these intensity profiles are in turn usedto expose a photosensitive recording medium, such as a xerographic photoreceptor, in accordance with the image defined by the successive pixelpatterns.

U.S. Pat. No. 4,940,314, issued Jul. 10, 1990, to D. L. Hecht, herebyincorporated by reference, addresses the problem that the effectivediameter of the pixels produced by an EO image bar, as measured betweentheir half power points at unity magnification, is approximatelyone-half the center-to-center spacing of its electrodes. Accordingly,such image bars not only tend to cause image distortion because ofspatial quantitization errors, but also characteristically produce interpixel intensity nulls.

To the extent possible, it is desired that there be an ON pixel for eachvoltage step between adjacent electrodes, and that individual pixels beof substantially the same shape and size regardless of the data pattern.Moreover, an EO image bar should be characterized by a high level oflight throughput and a modest level of required drive voltage. Size isan issue as well, with desired compactness militating toward shortelectrodes but ease of alignment militating toward long electrodes. Asis usually the case, it is difficult to achieve all these objectivessimultaneously. Attempts to optimize a given characteristic tend to leadto increased interpixel crosstalk or a degradation in some otherperformance characteristic.

SUMMARY OF THE INVENTION

The present invention provides a technique for reducing interpixelcrosstalk by selecting a particular electrode length and thus tailoringa portion of the spatial frequency response of the image bar. Theinvention is based in part on a recognition that the pixel size andquality resulting from a voltage difference between electrodes aredetermined primarily by the overall image bar spatial frequencyresponse, and that a set of preferred physical parameters can bedetermined by selecting parameter values to provide the desired spatialfrequency response. This is made possible by an improved understandingof the way that the physical parameters affect the frequency response.

In brief, it has been found that a desirable frequency response is onethat approximates sin(πPf) for absolute values of f less than about 1/P,where f is the spatial frequency and P is the minimum pixel pitch.Further, it has been found that a particular electrode length providesthe desired response for small absolute values of f. The particularelectrode length is approximately E^(1/2) P/γ were E is the ratio of thenormal to tangential dielectric tensor components, P is the minimumpixel pitch, and γ is the grazing angle. The desired cutoff in thefrequency response for absolute values of f above about 1/P can beachieved by selecting appropriate values for other physical parameters.

It has been found that the parameter values that optimize the spatialfrequency response do not necessarily optimize diffraction efficiency,and that other considerations might dictate non-optimum values. If it isdesired to use illumination conditions and electrode lengths that do notoptimize spatial frequency response, it is sometimes possible to obtainthe desired frequency response by using a compensation filter. Thefilter may be chosen to define the spatial frequency response over theentire range of relevant frequencies, depending on the other parameters.

A further understanding of the nature and advantages of the presentinvention may be realized by reference to the remaining portions of thespecification and the drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic side view of the optical train of a printerincorporating the present invention;

FIG. 2 is a schematic top view of the optical train of the printer;

FIG. 3 is a partly cut away bottom view of the electrooptic modulator;

FIG. 4 is a simplified block diagram of the electronic control system ofthe printer;

FIG. 5A shows schematically the electrode and pixel configuration withone electrode per pixel, and the minimum shift possible;

FIG. 5B shows the minimum shift possible with the configuration of FIG.5A;

FIG. 6A shows schematically the electrode and pixel configuration formultiple electrodes per pixel, and plots of electrical potential, phaseshift, and recorded pixel intensity;

FIG. 6B shows the minimum shift possible with the configuration of FIG.6A;

FIGS. 7A-C show various interlace patterns;

FIGS. 8A-H show the amplitude and frequency response for differentialencoding; and

FIG. 9A shows how portions of the modulator spatial frequency responseare tailored by selection of illumination conditions;

FIGS. 9B-C show how portions of the modulator spatial frequency responseare tailored by selection of electrode length according to the presentinvention; and

FIGS. 9D-H show how portions of the spatial frequency response aretailored by selection of an appropriate spatial filter.

DESCRIPTION OF SPECIFIC EMBODIMENTS System Overview

FIGS. 1 and 2 are schematic side and top views illustrating the opticaltrain of a line printer 10 having an EO spatial light modulator 12 forprinting an image on a photosensitive recording medium 13. As shown, therecording medium is a photoconductively coated drum 15 which is rotatedby any convenient drive mechanism in the direction of the arrow 17.Nevertheless, other xerographic and non-xerographic recording media,including photoconductively coated belts and plates, as well asphotosensitive films and coated papers could be used. Thus, in thegeneralized case, recording medium 13 should be visualized as being aphotosensitive medium which is exposed while advancing in a cross-lineor line pitch direction relative to modulator 12.

FIG. 3 is a partially cut-away bottom view of EO spatial light modulator12. In keeping with standard practices, the modulator comprises anoptically transparent EO element 20, such as an optically polished,y-cut crystal of lithium niobate, and a plurality of individuallyaddressable electrodes 22. Electrodes 22 are deposited on, or heldclosely adjacent, a longitudinal reflective surface 25 of EO element 20.For example, they may be integrated with their addressing and driveelectronics on a VLSI silicon circuit 27, and the modulator may then beassembled so that the electrodes are pressed against the reflectivesurface (by any convenient mechanism not shown). Typically, electrodes22 extend lengthwise along EO element 20 and are transversely spaced onmore or less uniformally displaced centers.

In operation, an illuminator 30 supplies a transversely collimated lightbeam 32 which is expanded by any convenient optical elements not shown)if and as required to illuminate substantially the full width of EOelement 20. This light beam is brought to a wedge-shaped focus at a neargrazing angle of incidence on the reflective surface of the EO elementand is totally internally reflected therefrom. Successive sets of datasamples are sequentially applied to electrodes 22, whereby the phasefront of light beam 32 is spatially modulated while passing through EOelement 20 in accordance with successive pixel patterns as a function oftime.

The beam direction relative to the EO modulator is characterized by agrazing angle γ and a skew angle θ. The grazing angle is the anglebetween the center of the beam and the plane of the reflecting surface,measured outside the modulator. The skew angle is the projected angle ofthe beam relative to the direction of the electrodes. The drawings showaxial operation (skew angle of zero).

A central dark field schlieren imaging system 35 (FIGS. 1 and 2)converts the phase modulated wavefront of light beam 32 into acorresponding intensity profile. The combination of modulator 12 withilluminator 30 and schlieren imaging system 35 is an example of what isreferred to herein as a discrete image bar 40.

A central dark field system suitably includes an objective lens 42 forfocusing the transversely collimated zero order diffraction componentsof light beam 32 (collectively represented by solid line rays in FIG. 2)onto an opaque stop 43. The distance between EO element 20 and lens 42is exaggerated. In a specific embodiment, the two are close so that lens42 acts as a field lens. The zero-order components of light beam 25 areblocked because the stop is centrally located in the rear focal plane ofthe field lens, but the higher order diffraction components(collectively represented by broken line rays in FIG. 2, together withbroken line cones for a single pixel) scatter around stop 43 and arecollected by an imaging lens 45. Lens 45, in turn, focuses them onrecording medium 13 with a predetermined magnification.

As will be described below, the imaging system may include acompensating spatial filter 47 located in a far field plane, which maybe the same plane as that of stop 43. Such a spatial filter would beused as one way to optimize the spatial frequency response of the imagebar in order to produce uniform pixels of the desired size.

FIG. 4 is a block diagram illustrating circuitry for communicating datato electrodes 22 and controlling illuminator 30. Basic timing for thecircuitry and the operations described below is established by a clockgenerator 58. An incoming data stream is input to a data buffer 65,encoded at a differential encoder 67, and communicated to addressdecoding circuitry 70. A controller 75 manages the data flow through thebuffer and encoder, and provides sequential addresses to decodingcircuitry 70 so as to cause a line of data to be applied to electrodes22 during a data loading interval. Voltages corresponding to the datavalues are held on the electrodes during a subsequent data holdinterval, and the illuminator is turned on and then off during the datahold interval to effect recording of the line of data. The process isthen repeated for subsequent lines.

Multiple Electrodes Per Pixel

FIGS. 5A and 5B illustrate the relationship of the pixels and electrodesin a typical prior art configuration. The top half of FIG. 5A shows apair of adjacent pixels 102 and 103 resulting from a pattern ofdifferentially encoded voltages on a set of electrodes 105, 107, 108,and 110 In this configuration, the pixels are characterized by acenter-to-center spacing of P (pixel pitch), which also corresponds tothe center-to-center spacing of the electrodes. Adjacent ON pixels areshown as touching circles, but it should be understood that theintensity distribution across a pixel is such that a typical pixel has afull width at half intensity of approximately P/2, so that the pixelsare characterized by interpixel nulls.

The data is differentially encoded so that an ON pixel is produced atlocations between electrodes that are at different voltages. Thevoltages on the electrodes in FIG. 5A are 0, V, 0, and 0, thus providingfor an ON pixel centered between electrodes 105 and 107, and one betweenelectrodes 107 and 108, as defined by the differential encoding of thesignal on the electrodes. As described above, ON pixels will be producedresulting from the modulation caused by the differential voltage betweenelectrodes 105 and 107 and between electrodes 103 and 108. Since thereis no voltage differential between electrodes 108 and 110, no ON pixelis formed. FIG. 5A also shows the approximate electrical potential atthe surface of EO element 20, the amplitude of the electro-optical phaseshift produced by the resultant electric field, and the opticalintensity resulting at the image plane of schlieren imaging system 35.

The minimum transverse shift of pixel locations is defined by theelectrode spacing. As shown in FIG. 5B, when the voltage pattern isshifted to the right by one electrode interval, a corresponding shift inthe pixel pattern occurs. Accordingly, when the desirability of shiftingpixel patterns by less than a full pixel width was recognized, the priorart utilized mechanical or dispersive means to effect the desireddisplacement.

FIGS. 6A and 6B show the electrode and pixel configuration, and theminimum shift possible when a multiple-electrode-per-pixel configurationaccording to the present invention is used. FIG. 6A shows a pair of ONpixels 112 and 113 resulting from a set of voltages on a set ofelectrode pairs 115a-b, 117a-b, 118a-b, and 120a-b. In this case, theelectrodes have a center-to-center spacing of P'=P/2, but the voltagedoes not change any more frequently than once every two electrodes.Thus, the minimum ON pixel center-to-center spacing is 2P' (=P). FIG. 6Aalso shows the electrical potential, electro-optical phase shiftamplitude, and optical intensity for this configuration.

FIG. 6B shows the resultant pixel pattern when the voltages are shiftedone electrode to the right. In this case, the pixels maintain the sameminimum pixel pitch P and size, but are shifted by a distance of P'(=P/2).

At first glance, it would appear that it would be possible to pack thepixels more closely together by allowing the separation of transitionsto be as close as the electrode pitch P'. However, the result could beexcessive interference between adjacent ON pixels.

While the specific example of two electrodes per pixel interval isillustrated, the technique is readily extended to any plurality of Nelectrodes per pixel (i.e. electrode pitch P' equals 1/N times theminimum pixel pitch P). In such case, the above mentioned constraint isthat the encoding must result in groups of at least N electrodes at thesame potential. However, there is no requirement that the groups ofelectrodes at the same potential be integral multiples of N. Thus, theenhanced addressability allows ON pixels at separations of other thanintegral multiples of NP', still subject to the constraint that theseparation of transitions be at least NP'.

The present invention may be used to implement interlacing. This is doneby uniformly spacing all pixel positions on one line by the pixelspacing P, and then shifting all pixel positions on succeeding lines bytranslating all pixel positions by an electrode interval (P/N). Thespecific case illustrated above, namely N=2, is of practical importancesince it enables two-line interlace. The significance of this is thatthe typical pixel size is approximately P/2 in diameter so that theinterlace allows filling of interpixel nulls. It is noted that thismethod does not inherently provide cross-scan image translation tocompensate for recording medium motion between successive scan lines.Unless the medium is stopped for each scan line group, the result is adiamond interlace raster as shown in FIG. 7A. Directly recordingrectangular raster data on the diamond lattice will result in systematiccross-scan displacement for alternate pixels along the interlaced lines.This may or may not be a serious effect, depending on image content,recording process, and visual effects. For example, modification todigitized font designs can be used to compensate for this. The diamondinterlace raster can be advantageous if the recorded information isappropriately spatially sampled or interpolated, as for example in anelectronic reprographics system where the read-in sample locations areinherently independent of image edge location.

FIG. 7B shows the result of interlace with cross-scan compensation.

FIG. 7C shows how the displacement effect can be made negligible byswitching the modulator back and forth rapidly between the interlaceddata sets. This could be implemented by rewriting the data lines, whichrequires increased modulator data input bandwidth, or by employing aVLSI driver chip with internal storage of the two interlaced lines'data.

Preferred Physical Configuration

The output image depends upon the input data voltage pattern on theelectrodes and the spatial frequency response of the overall opticalsystem. This is determined by the intrinsic frequency response of themodulator itself, and the frequency response of other portions of theoptical system, such as the spatial filter (if present). To the extentpossible, it is desired that there be an ON pixel for each voltage stepbetween adjacent electrodes, and that individual pixels be ofsubstantially the same shape and size regardless of the data pattern.

The intrinsic spatial frequency response of the modulator depends on thephysical properties of the modulator, including the electrical andoptical properties of the material and the electrode geometry (lengthand pitch). The overall frequency response also depends on theillumination conditions and the spatial filter. As will be discussedbelow it is possible to select a physical configuration that suppressescrosstalk and provides high efficiency and uniform pixel size and shape.

It is convenient to define normalized grazing and skew angles G₀ and S₀,in units of the inter-order angle (the separation of the 0th and 1stdiffraction orders), and to define normalized spatial frequency F, drivevoltage V_(T), and electrode length Q₀ as follows:

    G.sub.0 =γ/(λ/(nΛ.sub.0))

    S.sub.0 =θ/(λ/(nΛ.sub.0))

    F=fΛ.sub.0

    Q.sub.0 =2πLλ/(nΛ.sub.0.sup.2)

    V.sub.T =2πn.sup.4 rΛ.sub.0 V(f)/λ.sup.2

where

γ=grazing angle (the angle between the beam and the surface of theelectro-optic element)

θ=skew angle (the angle between the beam and the direction of theelectrodes)

f=spatial frequency

V(f)=peak-to-peak voltage of the TIR surface potential spectrumcomponent at spatial frequency f

L=electrode length

λ=optical wavelength

n=optical index of refraction

Λ₀ =EO spatial modulation period (2N times electrode pitch, or 2 timesminimum pixel pitch P)

The diffraction efficiency η as a function of spatial frequency forplanewave illumination can be approximated by combining the physicaloptics diffraction theory results for long electrode length, which givesproper results at high spatial frequencies, with a geometrical opticsdiffraction analysis for finite electrode length, which is valid for thelow spatial frequencies where total internal reflection diffractionsuppression effects are small. The resulting expression for η is asfollows:

    η=H.sub.Q.sup.2 V.sub.T.sup.2 E G.sub.0 * Re [(G.sub.0.sup.2 -2FS.sub.0 -F.sup.2).sup.1/2 ]/D

where

E=ratio of normal to tangential dielectric tensor components

    D={[(1-E)F+2S.sub.0 E].sup.2 +4EG.sub.0.sup.2 }.sup.2

    H.sub.Q= 1-exp [-|F|G.sub.0 Q.sub.0 /(2E.sup.1/2)].

The quantity V_(T) is a function of spatial frequency, being anormalized version of V(f) which is the peak-to-peak voltage of the TIRsurface potential component at spatial frequency f. The quantity dependson the data encoded on the electrodes since the data defines the spatialfrequencies that are present. For all pixels ON, the voltage alternatesfrom electrode to electrode so the spatial period is twice the pixelpitch, the spatial frequency is the inverse of this, and the normalizedfrequency F=1. In this case the value of V is approximately equal to theimpressed voltage, differing by a geometrical factor near unity thatdepends on the electrode width relative to the gap between electrodes.

It should be noted that the equation gives the first order diffractiontheory, which is valid for diffraction efficiencies up to about 30%.Beyond 30%, non-linear multiple scattering effects may become importantand the linear system frequency response analysis may not be sufficient.The amplitude of the frequency response is given by H(F)=η^(1/2)sgn(F)/V_(T).

Where differential encoding is used, it is desired that the diffractedlight optical amplitude at a point is proportional to the difference inelectrical potential between points spaced by the pixel pitch (which forthe case of N electrodes per pixel is N times the electrode pitch). Thiscalls for a response similar to the linear operator known as the finitedifference operator.

FIGS. 8A-B show an ideal step input and the finite difference responseto the step input taken over an interval P, where P is the pixel pitch.FIGS. 8C-D are corresponding views for a non-ideal step input. Thefinite difference operator Δ(P) can be expressed as an odd impulse pair,namely Δ(P)=δ(x+P/2)-δ(x-P/2), as shown in FIG. 8E.

The frequency response is given by the Fourier transform of the finitedifference operator. FIG. 8F shows the optimum frequency response foroperation with differential encoding. The response varies as sin(πF/2),where F=1 (f=1/(2P)) corresponds to the fundamental "all pixels ON"diffraction component. FIG. 8G shows an acceptable response, whichtracks the ideal response over the spatial frequency range -2≦F≦2 whereF=2 (f=1/P) is the first zero of the desired frequency response. For oneelectrode per pixel encoding, or for the more general case where all thenormalization is in terms of 2N times the electrode pitch (i.e., 2 timesthe pixel pitch) response at higher frequencies is not required, asthese components only contribute to pixel profile edge sharpness.

FIG. 8H shows the frequency response in the limit of long electrodes andlarge grazing angle. The response is substantially different from thefrequency dependence that is desired. It is, however, possible to tailorthe physical parameters to provide the desired frequency response.

In the long electrode limit, it can be shown that the efficiency at F=1is maximized at a relatively small grazing angle. However, for smallgrazing angles, the quantity (G₀ ² -2FS₀ -F²) becomes negative for somehigher but finite spatial frequencies, and therefore the response cutsoff above a finite spatial frequency. Fortunately, this cutoff can beexploited to bring the spatial frequency response of FIG. 8H more inline with that of FIG. 8G.

For axial illumination (S₀ =0), cutoff occurs when G₀ ≧F, i.e., when theinter-order diffraction angle for a given spatial frequency equals orexceeds the input grazing angle. Axial illumination is of particularinterest since the response is antisymmetric with respect to F asdesired for differential encoding. Using G₀ substantially less than 2would truncate part of the desired frequency response for differentialencoding below F=2. On the other hand, using G₀ substantially greaterthan 2 would reduce the diffraction efficiency and would make thefrequency response depart from the desired form below F=2 with a cutoffat F=2. Therefore, G₀ =2 and S₀ =0 is a preferred illumination conditionfor the differentially encoded modulator. FIG. 9A shows the spatialfrequency response for G₀ =2 and S=0, with a long electrode.

It is important to note that additional conditions are required toachieve the desired frequency response form in the frequency range-1≦F≦1. Two approaches to correcting this frequency response areselecting an optimum electrode length and providing a speciallyconfigured optical spatial frequency response filter.

If the electrode length is relatively short, the dependence of thefactor H_(Q) ² in the efficiency equation becomes apparent. In fact,H_(Q) is approximately linear as a function of F, which means that italso approximates a sinusoidal function of F for small values of F. FIG.9B shows the frequency response for a finite electrode length; this isclearly closer to the desired response. By selecting the appropriateelectrode length, it is possible to fit the frequency response to thedesired response in a low frequency region. More particularly, for F<<1,H_(Q) ≈sin(FG₀ Q₀ /(2E^(1/2))), which will equal sin(πF/2) for Q₀=πE^(1/2) /G₀. This provides the optimum frequency response, as shown inFIG. 9C. In terms of the physical variables this gives L=E^(1/2) Λ₀/(2γ)=E^(1/2) P/γ.

This optimum length is independent of the optical wavelength, so that inmulti-wavelength operation, frequency response can be simultaneouslyoptimized over a broad range of wavelengths. This is because theinteraction path truncation is a geometrical optics effect independentof wavelength. For operation in lithium niobate with the tangentialdirection along the z crystal axis and the normal direction along the ycrystal axis, E=1.54 if clamped dielectric constants are effective (2.54if unclamped dielectric constants are effective). For E=1.54, and G₀ =2,then the optimum value is Q₀ =1.95. In this case, H_(Q) =0.792 at F=1 sothat the efficiency for the "all pixels ON" condition for a givenvoltage is decreased by a factor H_(Q) ² =0.63 compared to a very longelectrode. Alternately, the compensating voltage increase is 1/H_(Q)=1.26. (For E=2.54 and G₀ =2, then Q₀ =2.50 and the other quantitiesscale accordingly). In general, the clamped dielectric constants applyto electrodes switched at high frequency above acoustic resonance;unclamped constants apply below acoustic resonance.

Thus, the dependence of the diffraction efficiency on electrode lengthallows the selection of an electrode length that provides the desiredspatial frequency response. However, the electrode length that optimizespixel crosstalk suppression is not necessarily the electrode length thatis desirable from other points of view. As noted above, the optimumelectrode length results in a decrease in efficiency and an increase inthe drive voltage required. Moreover, short electrodes may be difficultto align properly, thereby militating toward longer electrodes.

The discussion above is generally in terms of normalized variables, andthe statements regarding optimum length assume a fixed minimum pixelpitch P. However, it is possible to have physically long electrodes thatoptimize both efficiency and frequency response if it is permissible toincrease the pitch P (i.e. have the electrodes more widely spaced) whilemaintaining the normalized parameters the same.

To the extent that it is desired to use longer electrodes than arenecessary to optimize the low spatial frequency response of themodulator, it is possible to use a spatial filter (a compensationfilter) that provides the desired system response with long electrodes.Assuming the illumination conditions are chosen to result in a cutoff inthe modulator's response (as shown in FIG. 9A), the spatial filtershould have a transmission characteristic that approximates |sin(πF/2)|in amplitude and sin² (πF/2) in intensity for absolute values of F lessthan about 1. This can be expressed in terms of the actual physicalspatial dimension in the spatial frequency plane, x, by the scalingrelationship x=Z_(f) Fλ/(2P) where Z_(f) is the focal length ofobjective lens 42. FIGS. 9D and 9E show the amplitude and intensityprofiles for a compensation filter that could be used to provide thedesired frequency response. This corresponds to a pure absorptionfilter, and is readily realizable and applicable by such means as avariable density photographic emulsion.

Independent of these considerations, a stop is required to adequatelyattenuate the zero-order beam for sufficiently high contrast schlierenimaging. If the zero-order light is sufficiently collimated, thecompensation filter can perform the function of this stop since in theregion -0.1≦F≦0.1, the sine filter transmission is small (less than 1%).However, if the zero- order beam is not narrowly localized over theentire image field due to optical system aberration, an additional highabsorption stop may be employed. It need not be tapered because of thesimultaneous presence of the compensation filter.

If for some reason it is necessary to use non-optimum grazing angle andelectrode length, it is still possible to obtain the desired frequencyresponse solely by use of a compensation spatial filter. For example, inthe long-electrode, high-angle case, the filter should have atransmission characteristic that is proportional to |sin(πF/2)| inamplitude and sin² (πF/2) in intensity for |F|<2. FIGS. 9F and 9G showthe filter characteristics. This filter requires no absorption at thefundamental frequency (F=1) of the modulator (all pixels on response);the absorption reduces excess light and ringing in modulated patternpixels only. FIG. 9H is a simplified schematic view, which also showsblocking the light above |F|=2. It also shows the response relative tothe physical device.

CONCLUSION

In summary, it can be seen that the present invention provides atechnique for optimizing the spatial frequency response of EO spatiallight modulators by selecting an electrode length that provides thedesired low spatial frequency behavior.

While the above is a complete description of a number of embodiments,various modifications, alternatives, and equivalents may be used. Forexample, a central bright field system (not shown) could be used toperform the conversion process, although it will be understood that sucha change would reverse the logical relationship of the individual pixelswithin the intensity profile to the localized phase modulation of thewavefront of light beam 32 (i.e., "bright" pixels would become "dark"pixels, and vice-versa, unless steps were taken to account for thereversal in the logical relationship). In such a case, however, thespecific techniques for optimizing the spatial frequency response of theimage bar might be different.

Therefore, the above description should not be taken as limiting thescope of the invention which is defined by the appended claims.

What is claimed is:
 1. In a system that includes an electrooptic totalinternal reflection light modulator having a set of electrodes, anelectronic control subsystem for differentially encoding pixel data onthe electrodes by applying corresponding voltages thereto in a mannerthat defines a minimum pixel pitch P, an illumination subsystem forproviding an input beam to the modulator, which input beam is convertedto a phase front modulated beam by the modulator and the voltagesapplied thereto, and an imaging subsystem for converting the phase frontmodulated beam to an imaged beam having an intensity modulated profilecorresponding to the pixel data, wherein the diffraction efficiency ofthe system is in part defined by a set of properties of the modulatorand the illumination and imaging subsystems and is characterized by aspatial frequency response, the improvement wherein:the electrodes arecharacterized by a length chosen to cause the frequency response of themodulator to approximate sin(πPf) for small absolute values of f, wheref is the spatial frequency.
 2. The improvement of claim 1 wherein theelectrodes are equally spaced with an electrode pitch that is equal tothe minimum pixel pitch P.
 3. The improvement of claim 1 wherein theelectrodes are equally spaced with an electrode pitch that is anintegral fraction 1/N of the minimum pixel pitch P.
 4. The improvementof claim 1 wherein the input beam impinges on the modulator in adirection parallel to the electrodes and at a grazing angle chosen tocause the frequency response to cut off at absolute values of f aboveabout 1/P, whereupon the spatial frequency response of the systemapproximates sin(πPf) for absolute values of f less than about 1/P. 5.The improvement of claim 1 wherein:the input beam impinges on themodulator at a grazing angle γ; and the electrode length isapproximately E^(1/2) Pγ where E is the ratio of normal to tangentialdielectric components of the modulator.
 6. The improvement of claim 1wherein the input beam impinges on the modulator at a grazing angle thatis approximately λ/(nP) where λ is the optical wavelength and n is theoptical index of refraction.
 7. The improvement of claim 1 wherein:theinput beam impinges on the modulator in a direction parallel to theelectrodes and at a grazing angle γ chosen to cause the frequencyresponse to cut off at absolute values of f above about 1/P; and theelectrode length is approximately E^(1/2) Pγ where E is the ratio ofnormal to tangential dielectric components of the modulator.
 8. Theimprovement of claim 1 wherein:the input beam impinges on the modulatorat a grazing angle γ that is approximately λ/(nP) where λ is the opticalwavelength and n is the optical index of refraction; and the electrodelength is approximately E^(1/2) Pγ where E is the ratio of normal totangential dielectirc components of the modulator.